Uniqueness of Bogomol'nyi equations and Born-Infeld like supersymmetric theories

TL;DR

This paper demonstrates that Bogomol'nyi equations and bounds in gauge theories with Higgs scalars are universal across different gauge Lagrangians, including Maxwell and Born-Infeld, due to supersymmetry constraints.

Contribution

It reveals the universality of BPS equations in various gauge theories through supersymmetric analysis, regardless of the specific form of the gauge Lagrangian.

Findings

Bogomol'nyi equations are insensitive to the gauge Lagrangian form.

Supersymmetry dictates the BPS bounds and equations.

Maxwell and Born-Infeld theories share the same BPS structure.

Abstract

We discuss Bogomol'nyi equations for general gauge theories (depending on the two Maxwell invariants $F^{\mu \nu} F_{\mu \nu}$ and $\tilde F^{\mu \nu} F_{\mu \nu}$) coupled to Higgs scalars. By analysing their supersymmetric extension, we explicitly show why the resulting BPS structure is insensitive to the particular form of the gauge Lagrangian: Maxwell, Born-Infeld or more complicated non-polynomial Lagrangians all satisfy the same Bogomol'nyi equations and bounds which are dictated by the underlying supersymmetry algebra.